Statistical physics methods provide the exact solution to a long-standing problem of genetics

TL;DR

This paper applies statistical physics methods to derive exact probabilities for recombinant inbred lines in genetics, solving a long-standing problem for any number of genes using Glauber's formula and Schwinger-Dyson equations.

Contribution

It introduces a novel combination of physics-based probabilistic frameworks to solve a complex genetics problem previously unsolved for multiple genes.

Findings

Exact probabilities for RILs with any number of genes derived

Methods extend to applications in population genetics

Provides a new analytical approach for complex genetic models

Abstract

Analytic and computational methods developed within statistical physics have found applications in numerous disciplines. In this letter, we use such methods to solve a long-standing problem in statistical genetics. The problem, posed by Haldane and Waddington [J.B.S. Haldane and C.H. Waddington, Genetics 16, 357-374 (1931)], concerns so-called recombinant inbred lines (RILs) produced by repeated inbreeding. Haldane and Waddington derived the probabilities of RILs when considering 2 and 3 genes but the case of 4 or more genes has remained elusive. Our solution uses two probabilistic frameworks relatively unknown outside of physics: Glauber's formula and self-consistent equations of the Schwinger-Dyson type. Surprisingly, this combination of statistical formalisms unveils the exact probabilities of RILs for any number of genes. Extensions of the framework may have applications in population genetics and beyond.